I am pretty damn sure that your thermostat has "burned out". The thermostat clicks in and out over the years to switch the compressor on and off as required. Eventually the contacts burn and can stick together. (compressor constantly running). The burn smell is probably from there if the burning smell was within the fridge.
**** If you do check the thermostat, make sure you are unplugged from the mains.****
Adragon
August 2008